ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
163 
№ 
a(s,t) = (U(s,t)-m i )SC x + < l l (x)-P i (t),x(t) > 
b(s, t) = (V(s,t) - m 3 )SC y + < / 3 (*) - P 2 (/),3>(0 > 
2. Distortion of two polygons 
We should distort the line included in the two polygons. 
3. Displacement of polygon 
Displace points in lines related to this polygon. 
The special methods of 2 and 3 can be the same as 1. 
4. Point selection 
Filter the point information through the selection algorithm. 
For example, there are two classifications, consider the 
geometrical properties, first, computer the expectation 
of samples in co, and the expectation 
M, = 
x2 ] of samples in co . Then make the perpendicular 
M, = 
bisector of the two points and use the perpendicular bisector as 
the criterion function g(X). 
The linear equation is: 
2x(m xl ~m x2 ) + 2y(m yX -m y2 ) + m 2 x2 - m] x + m] 2 - m) x = 0 
is just the criterion function of Bayes classification when we 
suppose P{co x ) = P{co 2 ) = 0.5, p{X I co,) is the planar 
probability density function which obeys .That is: 
p(X/co,) = 
2 *l E 
T exp{ ^ }(/ = 1,2) 
(2.1) 
V 
This geometrical classification is rational because the Bayes 
classification is the best classification. 
There are still other means, because of the length of the 
paper,we don't give uncecessary details, just narrate simply as 
follows: 
5. Distort merging of two polygons 
Distort lines included in these two polygons, and change 
the geographic object signs of related strikethroughs by 
topological table. 
6. Combination of some regions 
7. Substitue polygon for point set, and change the 
topology of the corresponding polygon. 
8. Substitue one polygon for multi-polygon, and change 
the corresponding outer polygon. 
9. Elimination of the same region 
10. Scale-up the lines which composed the polygon, but 
don’t add the number of the lines. 
11. Enlarge the region needed to display, so that minish 
the corresponding polygon. 
12. Simplify the complicated information of lines’ shape. 
4. CONCLUSION 
Through these approaches above, we can resolve 12 kinds of 
geometrical deformation in map generalization. Because these 
approaches reserve the topological relations of geographic 
objects, it can resolve the varying map scale information 
automatic generalization in GIS preferably. 
5. REFERENCES 
Dan Liu, etc., 1999, A kind of Perception Algorithm, International 
Academic Publisher 
g(X) = W T X 
Flere, _ w _ f m* ] is the expectation of o) j , 2 is the 2x2 
x I is the 
07 
covariance matrix,|£|is the determinant of 2, ^ _ 
training sample ,and x,y with the same variance is statistical 
independence(correlation function p-Q ).That is: 
Marc van Kreveld, 1997,Twelve Computational Geometry 
Problems from Cartographic Generalization, 
http://www.geo.unizh.ch/ICA-bin/documents 
Yin lianwang et al.1999.Research on WebGIS Base Geospatial 
Information Generalization with Varying Map Scale. Journal of 
Image and Graphics